Personally I like it for it's uniqueness in the taste aspect, I can't off the top of my head think of anything I could say "Oh, this tastes like Uni", and I like the funky, briney taste, the texture caught me off guard the first time I tried it but not after, the appearence is absolutely no big deal to me. IMO I think uni is a love it or hate it kind of thing.

i'm normally turned off by "slimey", but i this case, while the surface may feel slimy, there is actually a firmness to the uni that i really enjoy. in fact, one of my favorite preps is uni with raw egg, which i guess is like doubly slimey.

what i love is the unique taste to it and the overtones of sweet and briny. hard to describe, but its probably my favorite sushi item.

one other thing, a lot of times the uni served at sushi places is utter crap. its why i tend not to get it unless i know the place is getting the good stuff. but when its not fresh or low quality, it can have a funky and metallic taste to it that i really dislike and can entirely ruin it for you.

You mention of raw egg brings to mind that in a discussion like this it might be useful to separate out the whole "exotic" factor. Even with a humble and familiar item like an egg, some people like to eat raw eggs while plenty of others, as the OP put it with respect to sea urchin, "can't bear how it looks, tastes, and feels." Some people think dill pickles are vile. I just don't understand the quest to overcome an aversion to something simply because one has read that some other people like it.